Question: Which of the following numbers is a factor of 175? ${2,4,7,11,14}$
By definition, a factor of a number will divide evenly into that number. We can start by dividing $175$ by each of our answer choices. $175 \div 2 = 87\text{ R }1$ $175 \div 4 = 43\text{ R }3$ $175 \div 7 = 25$ $175 \div 11 = 15\text{ R }10$ $175 \div 14 = 12\text{ R }7$ The only answer choice that divides into $175$ with no remainder is $7$ $ 25$ $7$ $175$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $7$ are contained within the prime factors of $175$ $175 = 5\times5\times7 7 = 7$ Therefore the only factor of $175$ out of our choices is $7$. We can say that $175$ is divisible by $7$.